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update notebook
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@looooo
looooo committed Jan 6, 2024
1 parent 1c53d09 commit 8657be7
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175 changes: 99 additions & 76 deletions examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb
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Expand Up @@ -425,43 +425,17 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 12,
"id": "0811a6d6-4544-4a99-b4bd-ba5cf6b9027e",
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{
"name": "stdout",
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"text": [
"-2.605082438917929\n",
"-2.5926567550137163\n",
"-2.576276171400715\n",
"-2.5572968584132614\n",
"-2.5371037205738425\n",
"-2.516988590529518\n",
"-2.497957291921094\n",
"-2.4810015545771567\n",
"-2.4665124345839313\n",
"-2.455011136367867\n",
"-2.4464950349176995\n",
"-2.4409613820509275\n",
"-2.438356798763718\n",
"-2.438428922923462\n",
"-2.4408671029182987\n",
"-2.445442245573777\n",
"-2.4521135558911062\n",
"-2.460220787391342\n",
"-2.469626739199975\n",
"-2.4799773695959573\n"
]
},
{
"data": {
"text/plain": [
"<Part::PartFeature>"
"<Shape object at 0x6000011f2df0>"
]
},
"execution_count": 6,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -474,16 +448,12 @@
"from pygears.transformation import numeric_transformation\n",
"\n",
"debug = False\n",
"def compute():\n",
" module = 1.\n",
" num_threads = 3\n",
" alpha = np.deg2rad(20.)\n",
"def compute_involute(module=1, teeth=15, height=5, worm_pitch_diameter=10, num_threads=1, alpha=np.deg2rad(20)):\n",
" x = 0.\n",
" r_w = 7.5\n",
" y_p = 5\n",
" r_w = module * teeth / 2\n",
" y_p = worm_pitch_diameter / 2\n",
" r_thales = r_w / 2.\n",
" y_thales = y_p + r_thales\n",
" height = 5.\n",
" \n",
" def length(y):\n",
" return (x**2 + y**2)**(0.5)\n",
Expand All @@ -493,12 +463,12 @@
" \n",
" def z(y, t):\n",
" r = length(y)\n",
" return module * num_threads * np.arcsin(x / r) / 2 + r * np.tan(alpha) + t\n",
" return - module * num_threads * np.arcsin(x / r) / 2 + r * np.tan(alpha) + t\n",
" # return r * np.tan(alpha) + t\n",
" \n",
" def dz_dy(y):\n",
" r = length(y)\n",
" return -module * num_threads * x * dlength_dy(y) / \\\n",
" return module * num_threads * x * dlength_dy(y) / \\\n",
" (2 * np.sqrt(1 - x ** 2 / r ** 2 ) * r ** 2) + \\\n",
" np.tan(alpha) * dlength_dy(y)\n",
" # return np.tan(alpha) * dlength_dy(y)\n",
Expand All @@ -519,9 +489,9 @@
"\n",
" def min_head(pars):\n",
" y, t = pars\n",
" r_0 = y_p - module # * (1 + clearence)\n",
" y_inner = r_0 * np.cos(np.arcsin(x / r_0))\n",
" return ddistance_yp_dy(y, t) ** 2 + (y - y_inner) ** 2\n",
" r_0 = y_p - 2 * module # * (1 + clearence)\n",
" # y_inner = r_0 * np.cos(np.arcsin(x / r_0))\n",
" return ddistance_yp_dy(y, t) ** 2 + (y - r_0) ** 2\n",
"\n",
" def analytic_solution_for_x_0():\n",
" t = - (r_w + y_p) * np.tan(alpha)\n",
Expand All @@ -536,69 +506,122 @@
" print(f\"normal analytic: {ddistance_yp_dy(start[0], start[1])}\")\n",
" print()\n",
"\n",
" # t_end is once computed for x=0\n",
" t_end = sp.optimize.minimize(min_head, [y_p, 0.]).x[1]\n",
"\n",
" xyz = []\n",
" for x in np.linspace(-height / 2, height / 2, 20):\n",
" xyz_section = []\n",
" t_start = sp.optimize.minimize(min_ground, start).x[1]\n",
" # t_end = sp.optimize.minimize(min_head, [y_p, 0.]).x[1]\n",
" t_end = 3\n",
" for t in np.linspace(t_start, t_end, 20):\n",
" # compute the transformation\n",
" T0 = numeric_transformation((y_p * np.tan(alpha) + np.sign(alpha) * module * np.pi / 4) / r_w,\n",
" np.array([0., 0., 1.]), \n",
" np.array([0., 0.,0.]))\n",
" T1 = numeric_transformation(np.pi / 2.,\n",
" np.array([0., 1., 0.]),\n",
" np.array([0., y_p + r_w, 0.]))\n",
" T2 = numeric_transformation(-t / r_w,\n",
" np.array([0., 0., 1.]),\n",
" np.array([0., 0., 0.]))\n",
" T = T0 @ np.linalg.inv(T2) @ np.linalg.inv(T1)\n",
"\n",
" # compute the time (t) dependent transformation\n",
" phi = np.pi / 2\n",
" phi += y_p * np.tan(alpha) / r_w\n",
" phi += - np.sign(alpha) * module * np.pi / 4. / r_w\n",
" phi += t / r_w\n",
" T_0 = numeric_transformation(phi, np.array([0., 0., 1.]))\n",
" T_1 = numeric_transformation(-np.pi / 2, np.array([0., 1., 0.]))\n",
" T_2 = numeric_transformation(0., np.array([0., 0., 1.]), np.array([0, y_p + r_w, 0.]))\n",
" T = np.linalg.inv(T_2 @ T_1 @ T_0)\n",
" \n",
" # find point on curve for given t\n",
" y = sp.optimize.minimize(distance_yp, y_p, (t)).x[0]\n",
" z_i = z(y, t) # - y_p * np.tan(alpha) + np.sign(alpha) * module * np.pi / 4\n",
" point = np.array([x, y, z_i, 1.])\n",
" xyz_section.append((T @ point)[:3])\n",
" xyz.append(np.array(xyz_section))\n",
"\n",
" return np.array(xyz)\n",
"\n",
"\n",
"curves = []\n",
"for line in compute().transpose(1, 0, 2):\n",
" bs = part.BSplineCurve()\n",
" points = [app.Vector(*point) for point in line]\n",
" bs.interpolate(points)\n",
" curves.append(bs.toShape())\n",
"\n",
"part.show(part.makeLoft(curves))"
" \n",
"# create two surfaces one for positive alpha and one for negative alpha\n",
"\n",
"for alpha in [np.deg2rad(- 20), np.deg2rad(20)]: \n",
" curves = []\n",
" for line in compute_involute(alpha=alpha).transpose(1, 0, 2):\n",
" bs = part.BSplineCurve()\n",
" points = [app.Vector(*point) for point in line]\n",
" bs.interpolate(points)\n",
" curves.append(bs.toShape())\n",
" part.show(part.makeLoft(curves))\n",
"\n",
"# create cutting survaces for head and bottom\n",
"# 1. compute strat and end of phi\n",
"\n",
"height = 5\n",
"worm_pitch_diameter = 10\n",
"teeth = 15\n",
"y_p = worm_pitch_diameter / 2\n",
"r_w = 7.5\n",
"module = 1.\n",
"clearence = 0.25\n",
"head = 0.\n",
"\n",
"r_head = y_p - module * (1 + head)\n",
"r_foot = y_p + module * (1 + clearence)\n",
"\n",
"phi_head = np.arcsin(height / 2 / r_head) # from + phi to - phi\n",
"phi_foot = np.arcsin(height / 2 / r_foot)\n",
"\n",
"line_head = []\n",
"for phi_i in np.linspace(-phi_head, phi_head, 10):\n",
" x = r_w + y_p - np.cos(phi_i) * r_head\n",
" z = np.sin(phi_i) * r_head\n",
" line_head.append([x, 0., z, 1])\n",
"\n",
"line_foot = []\n",
"for phi_i in np.linspace(-phi_head, phi_head, 10):\n",
" x = r_w + y_p - np.cos(phi_i) * r_foot\n",
" z = np.sin(phi_i) * r_foot\n",
" line_foot.append([x, 0., z, 1])\n",
"\n",
"curves_head = []\n",
"curves_foot = []\n",
"phi_j_max = 2 * np.pi / teeth\n",
"for phi_j in np.linspace(-phi_j_max, phi_j_max, 10):\n",
" T = numeric_transformation(phi_j, np.array([0., 0., 1.]))\n",
" temp_points_foot = [app.Vector(*(T @ point)[:3]) for point in line_foot]\n",
" temp_points_head = [app.Vector(*(T @ point)[:3]) for point in line_head]\n",
" bsp_foot = part.BSplineCurve()\n",
" bsp_head = part.BSplineCurve()\n",
" bsp_foot.interpolate(temp_points_foot)\n",
" bsp_head.interpolate(temp_points_head)\n",
" curves_foot.append(bsp_foot.toShape())\n",
" curves_head.append(bsp_head.toShape())\n",
"\n",
"part.show(part.makeLoft(curves_foot))\n",
"part.show(part.makeLoft(curves_head))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d804123e-3a1f-418a-b042-3619b1286c29",
"execution_count": 4,
"id": "5737ef53-ab3c-4ea4-98e7-09cfc111f956",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1, 2]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
"name": "stdout",
"output_type": "stream",
"text": [
"Help on function numeric_transformation in module pygears.transformation:\n",
"\n",
"numeric_transformation(angle, axis, translation=array([0., 0., 0.]))\n",
" see http://en.wikipedia.org/wiki/SO%284%29#The_Euler.E2.80.93Rodrigues_formula_for_3D_rotations\n",
" angle: angle of rotation\n",
" axis: the axis of the rotation\n",
" translation: translation of transformation\n",
"\n"
]
}
],
"source": [
"[1,2,3,4][:2]"
"help(numeric_transformation)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "012a264b-12b2-4fa3-a734-60251262e914",
"id": "cfcc64d4-3756-431d-a78b-a81d30c5f6db",
"metadata": {},
"outputs": [],
"source": []
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1 change: 0 additions & 1 deletion freecad/gears/timinggear_t.py
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Expand Up @@ -30,7 +30,6 @@

class TimingGearT(BaseGear):
def __init__(self, obj):
print("hello gear")
obj.addProperty("App::PropertyLength", "pitch", "base", "pitch of gear")
obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
obj.addProperty(
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